Zhi's Modest List of Publications


Papers Published in Journals and Books

  • Feng Guo and Chu Wangand Lihong Zhi
    Semidefinite Representations of Non-compact Convex Sets
    SIAM Journal on Optimization, 2014.
    SIAMOPGWZ.pdf
  • Yue Ma and Chu Wang and Lihong Zhi
    A Certificate for Semidefinite Relaxations in Computing Positive-Dimensional Real Radical Ideals
    Jouranl of Symbolic Computation, 2014.
    JSCMWZ.pdf
  • Nan Li and Lihong Zhi
    Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
    SIAM Journal on Numerical Analysis, 52(4):1623-1640, 2014.
    VMR.pdf
  • Zijia Li and Lihong Zhi
    Computing the Nearest Singular Univariate Polynomials with Given Root Multiplicities
    Theoretical Computer Science 479:163-173, 2013.
    LiZijiaZhiTCS.pdf
  • Nan Li and Lihong Zhi
    Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems: Case of Breadth One
    Theoretical Computer Science 479:150-162, 2013.
    LiZhiTCS.pdf
  • Nan Li and Lihong Zhi
    Computing isolated singular solutions of polynomial systems: case of breadth one
    SIAM Journal on Numerical Analysis, 50(1):354-372, 2012.
    LiZhi2011revised.pdf
  • Aurélien Greuet, Feng Guo, MohabSafey El Din and Lihong Zhi
    Global optimization of polynomials restricted to a smooth variety using sums of squares
    Journal of Symbolic Computation, 47:503-518, 2012.
    Preliminary version sos_vcg_final.pdf
  • Mohab Safey El Din and Lihong Zhi
    Computing rational points in convex semi-algebraic sets and sums of squares decompositions
    SIAM Journal on Optimization, 20(6):2876-2889, 2010.
    convex_sas.pdf
  • Nan Li and Lihong Zhi
    Computing the multiplicity structure of an isolated singular solution: case of breadth one
    Journal of Symbolic Computation, 47(6):700-710, 2012.
    finalversionLIZHI.pdf
  • Erich Kaltofen, Bin Li, Zhengfeng Yang, and Lihong Zhi
    Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients
    Journal of Symbolic Computation, 47(1):1-15, 2012.
    KLYZ09.pdf
  • Xiaoli Wu and Lihong Zhi
    Computing the multiplicity structure from geometric involutive form
    Journal of Symbolic Computation, 47(3):227-238, 2012.
    jsc_zhiwu.pdf
  • Bin Li, Jiawang Nie,and Lihong Zhi
    Approximate GCDs of polynomials and sparse SOS relaxations.
    Theoretical Computer Science, 409(2) pp.200-210, 2008.
    LNZTCS08.pdf
  • Greg Reid and Lihong Zhi
    Solving polynomials systems via symbolic-numeric eliminational method.
    Journal of Symbolic Computation, 44 pp.280-291, 2009.
    ReidZhiJSC08.pdf
  • Erich Kaltofen, John P. May, Zhengfeng Yang, and Lihong Zhi
    Approximate factorization of multivariate polynomials using singular value decomposition.
    Journal of Symbolic Computation, 43(5) pp.359-376, 2008.
    KMYZJSC08.pdf
  • Bingyu Li, Zhuojun Liu, and Lihong Zhi
    A Structured Rank-revealing Method for Sylvester Matrix
    Journal of Computational and Applied Mathematics,213 pp.212-223, 2008
    llzcam08.pdf
  • Bingyu Li, Zhuojun Liu, and Lihong Zhi
    AFast Algorithm for Solving the Sylvester Structured TotalLeast Squares Problem
    Signal Processing, 87 (2007) pp.2313-2319.
    llzsp07.pdf
  • Dongxia Sun and Lihong Zhi
    Structured Low Rank Approximation of a Bezout Matrix
    Mathematics in Computer Science, 2 (2007) pp.427-437.
    SunZhiMCS07.pdf
  • Bingyu Li, Zhengfeng Yang, and Lihong Zhi
    Fast Low Rank Approximation of a Sylvester Matrix by Structure Total Least Norm
    Journal of Japan Society for Symbolic and Algebraic Computation, 11(3,4) (2005) pp.165-174.
    lyzjssac05.ps
  • Robert M. Corless, Stephen M. Watt, and Lihong Zhi
    QR Factoring to Compute the GCD of Univariate Approximate Polynomials
    IEEE Transactions on Signal Processing, 52(12) pp.3394-3402, 2004.
    QRGCD.pdf
  • Lihong Zhi, Matu-Tarow Noda, Hiroshi Kai, and Wenda Wu
    Hybrid Method for Computing the Nearest Singular Polynomials
    Japan Journal of Industrial and Applied Mathematics, 21(2) pp.149-162, June 2004.
    znkwjjiam04.pdf
  • Lihong Zhi
    Hybrid Computation Lectures on Computer Algebra, (Ed. Dongming Wang, Lu Yang, Lihong Zhi, etc.), Tsing Hua Press, 2003.
    hybrid.pdf
  • Lihong Zhi
    Algebraic Factorization and GCD Computation
    Mathematics Mechanization and Applications, (Ed. Xiao-Shan Gao and Dongming Wang), Academic Press, 2000, pp 325-342.
    mmfac.pdf
  • K. Shiraishi H., Lihong Zhi, and Matu-Tarow Noda
    Implement of Wu's Method in Risa/Asir
    Journal of Japan Society for Symbolic and Algebraic Computation, 7(3) (1999) pp.41-42(abstract).
  • H. Minaguchi, Lihong Zhi , Hiroshi Kai and Matu-Tarow Noda
    Apply General Inverse of Matrix to Compute Nearest Singular Polynomials
    Journal of Japan Society for Symbolic and Algebraic Computation, 7(3) (1999) pp.29-30(abstract).
  • Lihong Zhi and Zhuojun Liu
    The P-irreducibility of Binding Polynomials
    An International Journal of Computers & Mathematics with Applications, 38(2) (1999) pp.1-10.
    pirr.pdf
  • Lihong Zhi and Wenda Wu
    Nearest Singular Polynomials
    Journal of Symbolic Computation, 26(6) pp.667-676, December 1998.
    nsp.pdf
  • Lihong Zhi
    An Optimal Method for Algebraic Factoring
    Journal of Computer Science and Technology, 12 pp. 1-9, January 1997.
    opfac.pdf

Papers Published in Conference Proceedings

  • Zhiwei Hao, Erich L. Kaltofen, and Lihong Zhi
    Numerical sparsity determination and early termination
    In ISSAC'2016 Proc. 2016 Internat. Symp. Symbolic Algebraic Comput.
    HKZ2016.pdf
  • Feng Guo, Mohab Safey El Din, Chu Wang, and Lihong Zhi
    Optimizing a parameteric linear function over a non-compact real algebraic variety
    In ISSAC'2015 Proc. 2015 Internat. Symp. Symbolic Algebraic Comput.
    GSWZ2015.pdf
  • Feng Guo, Chu Wang, and Lihong Zhi
    Optimizing a Linear Function over a Noncompact Real Algebraic Variety
    In SNC'2014 Proc. SNC Internat. Symp. Symbolic-Numeric Computation.
    GWZ2014SNC.pdf
  • Qingdong Guo, Mohab Safey El Din, and Lihong Zhi
    Computing rational solutions of linear matrix inequalities
    In ISSAC'2013 Proc. 2013 Internat. Symp. Symbolic Algebraic Comput.
    GuoSafeyZhiISSAC2013.pdf
  • Zhengfeng Yang, Lihong Zhi, and Yijun Zhu
    Verfied error bounds for real solutions of positive-dimensional polynomial systems
    In ISSAC'2013 Proc. 2013 Internat. Symp. Symbolic Algebraic Comput.
    YangZhiZhuISSAC2013.pdf
  • Feng Guo, Erich Kaltofen, and Lihong Zhi
    Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions
    In ISSAC'2012 Proc. 2012 Internat. Symp. Symbolic Algebraic Comput. pp. 195-202
    URL: http://arxiv.org/abs/1203.0253.
  • Yue Ma and Lihong Zhi
    Computing Real Solutions of Polynomial Systems via Low-Rank Moment Matrix Completion In ISSAC'2012 Proc. 2012 Internat. Symp. Symbolic Algebraic Comput. pp. 249-256
    MaZhiISSAC2012.pdf
  • Yue Ma and Lihong Zhi
    The Minimum-Rank Gram Matrix Completion via Modified Fixed Point Continuation Method
    In ISSAC'2011 Proc. 2011 Internat. Symp. Symbolic Algebraic Comput. pp. 241-248
    MaZhiISSAC2011.pdf
  • Sharon Hutton, Erich Kaltofen, and Lihong Zhi
    Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of seidenberg¡¯s method
    In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 227-234
    p227-hutton.pdf
  • Zijia Li, Zhengfeng Yang, and Lihong Zhi
    Blind image deconvolution via fast approximate GCD
    In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 155-162
    55_paper.pdf
  • Feng Guo, Mohab Safey El Din, and Lihong Zhi
    Global optimization of polynomials using generalized critical values and sums of squares
    In ISSAC'2010 Proc. 2010 Internat. Symp. Symbolic Algebraic Comput. pp. 107-114
    p107-guo.pdf
  • Xiaoli Wu and Lihong Zhi
    Computing the multiplicity structure from geometric involutive form
    In ISSAC'08 Proc. 2008 Internat. Symp. Symbolic Algebraic Comput. pp. 325-332
    WuZhiISS08.pdf
  • Erich Kaltofen, Bin Li, Zhengfeng Yang, and Lihong Zhi
    Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars.
    In ISSAC'08 Proc. 2008 Internat. Symp. Symbolic Algebraic Comput. pp. 155-163
    KLYZISS08.pdf
  • Erich Kaltofen, Zhengfeng Yang, and Lihong Zhi
    On Probabilistic Analysis of Randomization in Hybrid Symbolic-Numeric Algorithms
    In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.   pp. 11-17
    KYZsnc07.pdf
  • Erich Kaltofen, Bin Li, Kartik Sivaramakrishnan, Zhengfeng Yang, and Lihong Zhi
    Lower Bounds for Approximate Factorizations via Semidefinite Programming(extended abstract)
    In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.   pp. 203-204
    KLSYZsnc07.pdf
  • Bin Li, Jiawang Nie, and Lihong Zhi
    Approximate GCDs of Polynomials and SOS Relaxation (extended abstract)
    In Proc. 2007 Internat. Workshop on Symbolic-Numeric Comput.   pp. 205-206
    lnzsnc07.pdf
  • Lihong Zhi
    Numerical Optimization in Hybrid Symbolic-numeric Computation (extended abstract)
    In Proc. 2007 Internat. Workshop on Symbolic-NumericComput.pp. 33-35
    zhisnc07.pdf
  • Erich Kaltofen and Lihong Zhi
    Hybrid Symbolic-numeric Computation
    In ISSAC'06 Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. pp. 7
    KZiss06.pdf
  • Erich Kaltofen, Zhengfeng Yang, and Lihong Zhi
    Approximate Greatest Common Divisors of Several Polynomials with Linearly Constrained Coefficients and Singular Polynomials
    In ISSAC'06 Proc. 2006 Internat. Symp. Symbolic Algebraic Comput. pp. 169-176
    KYZiss06.pdf
  • Bingyu Li , Zhuojun Liu, and Lihong Zhi
    A Structured Rank-revealing Method for Sylvester Matrix
    Conference on Applications of Computer Algebra, July 31-August 3, 2005
  • Bingyu Li , Zhuojun Liu, and Lihong Zhi
    Fast Low Rank Approximation of a Sylvester Matrix
    In Dongming Wang and Lihong Zhi, editors, International Workshop on Symbolic-Numeric Computation SNC 2005 Proceedings, pp. 202-208, 2005
    LLZsnc05.ps
  • Erich Kaltofen, Zhengfeng Yang, and Lihong Zhi
    Structured Low Rank Approximation of a Sylvester Matrix
    In Dongming Wang and Lihong Zhi, editors, International Workshop on Symbolic-Numeric Computation SNC 2005 Proceedings, pp. 188-201, 2005
    KYZsnc05.ps
  • Greg Reid and Lihong Zhi
    Solving Nonlinear Polynomial System via Symbolic-Numeric Elimination Method
    Proceedings of international conference on polynomial system solving£¬pp. 50-53£¬ 2004
    rzicpss04.pdf
  • Greg Reid, Jianliang Tang, Jianping Yu, and Lihong Zhi
    Hybrid method for solving new pose estimation equation system
    Proceedings of the 2004 International Workshop on Computer and Geometric Algebra with Applications, LNCS 3519, H. Li et al. (eds), Springer Berlin Heidelberg, pp.46-57, 2005.
    rtyz04.pdf
  • Shuhong Gao, Erich Kaltofen, John P. May, Zhengfeng Yang, and Lihong Zhi
    Approximate factorization of multivariate polynomials via differential equations.
    Proceedings of the 2004 International Symposium on Symbolic and Algebraic Computation, pp. 167-174, 2004. ACM SIGSAM's ISSAC 2004 Distinguished Student Author Award (May and Yang).
    GKMYZ04.pdf
  • Joe Bonasia, Francois Lemaire, Greg Reid, Robin Scott, and Lihong Zhi
    Determination of approximate symmetries of differential equations
    In Gomez-Ullate (ed.), CRM Proceedings and Lecture Notes 39: 233-249, Amer. Math. Soc, 2004.
    ApproxSym.pdf
  • Lihong Zhi
    Displacement Structure in Computing the Approximate GCD of Univariate Polynomials
    Mathematics, pp.288-298, W.Sit and Z. Li(eds), World Scientific (Lecture Notes Series on Computing) 2003.
    displacement.pdf
  • Greg Reid, Jianliang Tang, and Lihong Zhi
    A Complete Symoblic-Numeric Linear Method for Camera Pose Determination
    Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pp. 215-223, 2003.
    trzissac03.pdf
  • Lihong Zhi, M.-T Noda, and K. Li
    On the construction of PSE for GCD Computation
    Proceedings of the Asian Symposium on Computer Mathematics, pp.76-81, World Scientific (Lecture Notes Series on Computing) 2001.
  • Kai Li, Lihong Zhi, and Matu-Tarow Noda
    Solving Approximate GCD of Multivariate Polynomials By Maple/Matlab/C Combination
    Proceedings of the Asian Technology Conference in Mathematics, pp.492-499, Chiangmai, Thailand, 2000.
    znlatcm00.pdf
  • Lihong Zhi and M.-T. Noda
    Approximate GCD of Multivariate Polynomials
    Proceedings of the Asian Symposium on Computer Mathematics, pp.9-18, Chiangmai, Thailand, 2000.
    znascm00.pdf
  • Yuzhen Huang, H.J.Stetter , Wenda Wu, and Lihong Zhi
    Pseudofactors of Multivariate Polynomials
    Proceedings of the 2000 International Symposium on Symoblic and Algebraic Compuation, pp.161-168. St. Andrews United Kingdom, 2000.
    HSWZISS00.ps
  • Lihong Zhi , Y. Notake, H. Kai, and M.-T. Noda
    Hybrid Method for Solving Polynomial Equations
    Proceedings of the Asian Technology Conference in Mathematics, pp.492-501, Guangzhou, China, 1999.
    atcm99.pdf
  • Lihong Zhi and Wenda Wu
    Nearest Singular Polynomials I
    Proceedings of the Asian Technology Conference in Mathematics, pp.323-332, Tsukuba, Japan, 1998.
  • Dongming Wang and Lihong Zhi
    Algebraic Factorization Applied to Geometric Problems
    Proceedings of the Asian Symposium on Computer Mathematics, pp.23-36, Lan Zhou, China, 1998.
    zwfac.pdf
  • Lihong Zhi and Wenda Wu
    A Note on Small Perturbations to Polynomials(abstract)
    Proceedings of the Asian Technology Conference in Mathematics, Penang, Malaysia, 1997.
  • Kai Huang, Dingkang Wang, and Lihong Zhi
    Wu method and its Applications (abstract)
    Proceedings of the Asian Technology Conference in Mathematics, Penang, Malaysia, 1997.
    hwzatcm97.pdf
  • Dingkang Wang and Lihong Zhi
    Software Development in MMRC
    Proceedings of the Asian Technology Conference in Mathematics, Singapore, December 18-21, 1995, pp 234-243.
    sdmmrc.pdf

Posters

  • R. Corless, S. Watt, and Lihong Zhi
    QR Factorization for Computing Approximate GCD
    The 2002 International Symposium on Symbolic and Algebraic Computation, 2002.
  • Iyad A. Ajwa and Lihong Zhi
    CharSets: An Efficient Implementation of the Characteristic Sets Method
    The Fifth Annual East Coast Computer Algebra Day, ECCAD '98, United States Naval Academy, Annapolis, Maryland, April 25, 1998.

Technical Reports


Dissertation

  • Lihong Zhi
    Polynomial Factorization over Algebraic Fields and its Applications
    Ph.D. Dissertation, Institute of Systems Science, Academia Sinica, Beijing, China, July 1996.


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lzhi@mmrc.iss.ac.cn